Question

0.
One of the exterior angle of a triangle is 105° and the interior opposite angles are in the
ratio 2:5. Find the angles of the triangle.
​

Answer 1

Answer:

let the ratio be 2x and 5x

105 + 2x +3x = 180

105+ 5x=180

5x = 180 - 105

5x = 75

X = 75/5

X = 15

2x = 2*15

= 30

3x = 5*15

= 75

Answer 2

Answer :

• The angles of a triangle are 30⁰ , 75⁰ , 75⁰

Given :

• One of the exterior angle of a triangle is 105⁵
• Interior opposite angles are in the ratio 2:5

To find :

• The angles of the triangle

Solution :

• Let the two angles be 2x and 5x

As we know that ,

• Sum of two interior opposite angles is equal to exterior angles

》 2x + 5x = 105

》 7x = 105

》 x = 105/7

》 x = 15⁰

Now putting the value in 2x and 5x we get ,

• 2x = 2(15) = 30⁰
• 5x = 5(15) = 75⁰

Now,

• Let the third angle of triangle be y

As we know that,

• Sum of all angles in a triangle is 180⁰

》30 + 75 + y = 180

》105 + y = 180

》 y = 180 - 105

》 y = 75

Hence , The angles of a triangle are 30⁰ , 75⁰ , 75⁰